Add colour to a cut meshface in animation
This works out of the box with the boolean modifer:


add your boolean modifier, don't apply it (this way you can use it in animations)
add a second material, the one to be assigned to the cut-off parts
change the order of the material so that the one created in 2. becomes the first material in the list.


This way, it will be assigned only to the cut-off faces created dynamically by the boolean modifier: